# Life tables

The basic data for our calculations comes as a table of death rates.

AgeMalesFemales
0 .00844 .00664
1 .00069 .00053
2 .00046 .00034
10 .00013 .00010
20 .00140 .00050
30 .00153 .00050
40 .00193 .00095
50 .00567 .00305
60 .01299 .00792
70 .03473 .01764
80 .07644 .03966
90 .15787 .11250
100 .26876 .23969

Notice the death rate for 10 year old females is only 1 in 10,000. So if you could stay a 10 year old girl, you would live till about 10,000 years of age! (Unfortunately, your 10 year old boy friend would pre-decease you by a few thousand years.)

The following are standard definitions used in this field:

```Let
q(x) = probability that a person will die within one year of age x

l(x) = fraction of those still alive at age x
l(0) = 1			everyone alive at age 0
l(x) = l(x-1) (1-q(x-1))        number alive at x is number at x-1
times (1 - probability) of death

d(x) = l(x) q(x)		number of deaths in year x

L(x) = number of lives lived between year x and x+1
L(x) = l(x) - d(x)/2		people who die live on average a half year

e(x) = life expectancy for a person of age x
e(x) = Sum_{i=x,inf} L(i)  / l(x)
```

The above definitions should help you understand our life table. (It came from the Center on the Economics and Demography of Aging of Berkeley.)